Question

(5.26) An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas usedy (in cubic feet) to heat the home and outside temperaturer( in degree- days, where a day's degree-days are the number of degrees its average temperature falls below 65 F) over a 23-month period. He then computed the least-squares regression line for predictingyfromxand found it to be: у 89 + 15 х The predicted amount of gas used when the outside temperature is 16 degree-days is about:cubic feet. (Answer to the nearest cubic foot) cBook Hint (5.30) A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)" Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this birc is: DD2.66 0,01 D, What is the slope of the regression line? (Round your answer to the nearest hundredth.) This means that on average, if the length of the dive increases by one meter, the diving duration increases by minutes. (Round your answer to the nearest hundredth) According to the regression line, how long does a typical dive to a depth of 194 meters last? minutes. (Round your answer to the nearest tenth.) Hint Check Syntax

Answer 1

5.26
y = 89 + 15x
y = 89 + 15(16)=329

5.30

Slope of the regression line = 0.01
If the lenght o fthe dive increases by one meter, the diving duration incerases by 0.01 minutes

DD = 2.66 + 0.01D
D = 194
DD = 2.66 + 0.01(194) = 4.6 minutes